[Proof of Theorem REF ]
Let \(n\ge 0\)  be an integer.
Recall that the \(n^{\text{th}}\)  skeleton \(\mathrm {sk}_n M\)  of \(M\)  comes
equipped with a map \(\mathrm {sk}_n M\rightarrow M\)  and that there are natural maps \(\mathrm {sk}_n M\rightarrow \mathrm {sk}_m M\)  whenever \(m\le n\) .
Recall also that \(M = \operatornamewithlimits{\mathrm {colim}}_n \mathrm {sk}_n M\)  and that \(\mathrm {sk}_{n-1}M\rightarrow \mathrm {sk}_nM\) 
fits into a pushout diagram built out of the \(n^{\text{th}}\)  latching object \(L_n M\)  of \(M\) . For more details we refer to
Chapter VII of [1]}.
